Diffusion模型

参数说明

beta_schedule = np.linspace(0.0001, 0.02, 1000)  # 示例 beta schedule

alpha_hat = np.cumprod(1 - beta_schedule)  # 计算 alpha_hat

具体例子

让我们通过一个具体的例子展示如何计算 Beta Schedule 和 Alpha_hat：

import numpy as np# 定义 Beta Schedule
beta_schedule = np.linspace(0.1, 0.2, 10)  # 从0.1到0.2等间隔分成10个值# 计算 Alpha_hat
alpha_hat = np.cumprod(1 - beta_schedule)# 打印结果
print("Beta schedule:", beta_schedule)
print("Alpha_hat:", alpha_hat)

在代码中的应用

def encode(x_0, t, alpha_hat):alpha_hat_t = alpha_hat[t]  # 获取时间步 t 的 alpha_hatepsilon = torch.randn_like(x_0)  # 生成标准正态分布噪声epsilon_prime = torch.sign(x_0) * torch.abs(epsilon)  # 计算符号噪声x_t = torch.sqrt(alpha_hat_t) * x_0 + torch.sqrt(1 - alpha_hat_t) * epsilon_prime  # 计算时间步 t 的特征向量return x_tfor t in range(num_steps):x_t = encode(x_0, t, alpha_hat)node_features.append(x_t.numpy())print(f"Node features at time step {t+1} (x_{t+1}):", x_t.numpy())

反向扩散过程和损失计算

for t in range(num_steps-1, -1, -1):x_t = torch.tensor(node_features[t+1])mu_theta, sigma_t = model.decode(x_t, t, alpha_hat)print(f"Reconstructed features at time step {t} (mu_theta_{t}):", mu_theta.detach().numpy())

完整的代码

import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np定义模型类
class DiffusionModel(nn.Module):def __init__(self, d):super(DiffusionModel, self).__init__()self.epsilon_predictor = nn.Sequential(nn.Linear(d, d),nn.ReLU(),nn.Linear(d, d))def decode(self, x_t, t, alpha_hat):alpha_hat_t = alpha_hat[t]mu_theta = self.epsilon_predictor(x_t)sigma_t = torch.sqrt(1 - alpha_hat_t)return mu_theta, sigma_tdef encode(x_0, t, alpha_hat):alpha_hat_t = alpha_hat[t]epsilon = torch.randn_like(x_0)epsilon_prime = torch.sign(x_0) * torch.abs(epsilon)x_t = torch.sqrt(alpha_hat_t) * x_0 + torch.sqrt(1 - alpha_hat_t) * epsilon_primereturn x_t, epsilondef compute_total_loss(model, x_0, alpha_hat):num_steps = len(alpha_hat)x_t = x_0epsilon_list = []多步噪声传递过程for t in range(num_steps):x_t, epsilon = encode(x_t, t, alpha_hat)epsilon_list.append(epsilon)total_loss = 0反向扩散过程for t in range(num_steps-1, -1, -1):mu_theta, sigma_t = model.decode(x_t, t, alpha_hat)epsilon_t = epsilon_list[t]total_loss += F.mse_loss(mu_theta, epsilon_t)更新 x_t 为上一步的特征x_t = (x_t - torch.sqrt(1 - alpha_hat[t]) * epsilon_t) / torch.sqrt(alpha_hat[t])return total_loss初始化参数
d = 5  # 特征向量维度
beta_schedule = np.linspace(0.1, 0.2, 10)  # 示例 beta 计划
alpha_hat = np.cumprod(1 - beta_schedule)  # 计算 alpha_hat初始化节点特征向量
x_0 = torch.tensor([1.0, 2.0, 3.0, 4.0, 5.0])
print("Initial node features (x_0):", x_0.numpy())初始化模型
model = DiffusionModel(d)计算总损失
total_loss = compute_total_loss(model, x_0, alpha_hat)
print("Total loss:", total_loss.item())